Topological phases of a non-Hermitian coupled SSH ladder

We study topological phases of a non-Hermitian coupled Su-Schrieffer-Heeger (SSH) ladder. The model originates from the brick-wall lattices in the two-row limit. The Hamiltonian can be brought into block off-diagonal form and the winding number can be defined with the determine of the block off-diagonal matrix. We find the determine of the off-diagonal matrix has nothing to do with the interleg hopping of the ladder. So the topological phases of the model are the same as those of the chains. Further numerical simulations verify the analysis.